Question Video: Converting Units of Atmospheric Pressure Physics

If the pressure of a contained gas in a tank is 2.3 atm, what is its pressure in centimeters of mercury? Let 𝑃_(𝑎) = 76 cm Hg.

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Video Transcript

If the pressure of a contained gas in a tank is 2.3 atmospheres, what is its pressure in centimeters of mercury? Let 𝑃 sub 𝑎 equal 76 centimeters of mercury. (A) 174.8 centimeters of mercury, (B) 33.0 centimeters of mercury, (C) 141.8 centimeters of mercury, or (D) 93.1 centimeters of mercury.

To answer this question, we need to convert the value of the gas pressure from units of atmospheres to units of centimeters of mercury. We are told that the value of 𝑃 sub 𝑎, which stands for atmospheric pressure, is equal to 76 centimeters of mercury. This means that in normal atmospheric pressure, which is equal to one atmosphere, the mercury in a barometer will be at a height of 76 centimeters. But if the barometer were placed in a higher-pressure environment, the mercury would rise higher up the tube. This is because there is a greater pressure pushing down on the mercury in the dish and pushing it up the tube. So, a higher pressure corresponds to a greater number of centimeters of mercury.

To answer this question, we need to work out how many centimeters of mercury is equivalent to 2.3 atmospheres.

Let’s start by writing down what we already know. At atmospheric pressure, the pressure is equal to one atmosphere, which is equivalent to 76 centimeters of mercury. In the gas tank, the pressure is equal to 2.3 atmospheres. In other words, the pressure in the gas tank is 2.3 times higher than the atmospheric pressure. So, the value of the pressure, when given in units of centimeters of mercury, must also be 2.3 times higher than at atmospheric pressure.

So, in units of centimeters of mercury, the pressure of the gas in the tank is simply equal to 76 centimeters of mercury multiplied by 2.3. This gives us a pressure of 174.8 centimeters of mercury. So, the correct answer to this question is option (A).